Experimental set up
A compound channel setup was used for this case study. The paper
including all information about the experience was found in Proust and Nikora (2020), data are available
in PROUST and NIKORA (2025).
- Length: 18 m
- Width: 3 m
- Slope: 0.0011
- Main channel: 1 m wide rectangular glass bed
- Floodplain: two 1 m wide flat rough-surface covered with dense
artificial grass (consisting of 1 mm wide and 5 mm high thin rigid
blades, with a density of 256 blades per square centimeter).
- Vertical distance from the main channel to the floodplain: 0.117
m
- Flow conditions: uniform flow with a total discharge of 114 L/s, of
which 8 L/s passed through the floodplain
- Water level measurements: taken at spatial intervals of 0.3 to 1 m
along the streamwise direction, at transverse positions at y=0.3 and 0.7
m on the right-hand floodplain and at y=1.2, 1.5 and 1.8 m in the main
channel.
Main features for the estimation
- A friction coefficient is estimated in the main channel and other
one in the floodplain.
- A constant longitudinal friction is considered.
- No more polynomial degrees have been performed.
- A single event is used for the calibration. The observed WSE is
taken from the average of the measurements in the main channel and the
floodplain.
- Experiments performed have just changed the observational data to
answer some questions about the identifiability of the friction
coefficients in the main channel and the floodplain.
- In the real case, upstream discharge was divided between the main
channel and the floodplain. In the model, a total discharge is
considered without any distinction.
- Measurement of WSE were taken in the main channel and the
floodplain. For this case, an average value was calculated for each
cross-section to compare with the simulations. All averaged depth values
were converted to elevation using the downstream as the reference
datum.
- Uncertainty of the observations was calculated using a regression
function passing through the water depth and then a standard deviation
was calculated for all observations.
- No measurements of the downstream threshold were reported.
Therefore, the last available measurements were taken to define the
downstream boundary condition in the model.
Laboratory measurements
Take a look about all the measurements:
Experiment: 1_WSE_floodplain_realistic_uncertainty
Here the experiment with the observational data obtained in the
laboratory,averaging the values of the WSE.
Calibration data
A sample was taken of all measurements shown previously: 
Corelation plot of MCMC cooked:
Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2001.0000000 |
2001.000000 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2001.000000 |
2001.000000 |
| Minimum |
107.4760000 |
23.356700 |
1.50000e-06 |
5.350170 |
5.473510 |
7.743410 |
6.253130 |
| Maximum |
130.0730000 |
46.343400 |
1.75630e-03 |
17.402300 |
22.259300 |
30.763900 |
27.444300 |
| Range |
22.5970000 |
22.986700 |
1.75480e-03 |
12.052100 |
16.785800 |
23.020500 |
21.191200 |
| Mean |
120.2120000 |
32.501500 |
2.06800e-04 |
10.045000 |
10.231900 |
15.379100 |
15.357700 |
| Median |
119.6200000 |
32.874100 |
1.71700e-04 |
9.793080 |
10.025000 |
15.268400 |
15.098500 |
| Q10% |
114.0310000 |
26.350600 |
3.29000e-05 |
7.671800 |
7.533980 |
11.570400 |
11.315500 |
| Q25% |
116.5180000 |
28.121200 |
6.60000e-05 |
8.672890 |
8.635640 |
13.172900 |
12.937500 |
| Q75% |
124.5030000 |
36.109800 |
3.06300e-04 |
11.206600 |
11.669000 |
17.080600 |
17.506600 |
| Q90% |
126.5360000 |
38.714200 |
4.31000e-04 |
12.853100 |
13.112000 |
19.466900 |
19.593900 |
| St.Dev. |
4.8327100 |
4.779110 |
1.78100e-04 |
1.971020 |
2.200820 |
3.108970 |
3.275740 |
| Variance |
23.3551000 |
22.839900 |
0.00000e+00 |
3.884940 |
4.843600 |
9.665710 |
10.730500 |
| CV |
0.0402015 |
0.147042 |
8.61514e-01 |
0.196220 |
0.215094 |
0.202156 |
0.213297 |
| Skewness |
0.0730142 |
0.104323 |
2.22869e+00 |
0.635261 |
0.571186 |
0.611240 |
0.543355 |
| Kurtosis |
-0.9667830 |
-0.821106 |
1.15867e+01 |
0.351366 |
0.620198 |
1.211530 |
0.343737 |
| MaxPost |
119.8560000 |
32.305200 |
6.37000e-05 |
10.483900 |
9.980640 |
13.988500 |
15.570500 |
| St.Dev. |
4.83271 |
4.77911 |
0.1781380 |
1.97102 |
2.20082 |
3.10897 |
3.27574 |
| MaxPost |
119.85600 |
32.30520 |
0.0636728 |
10.48390 |
9.98064 |
13.98850 |
15.57050 |
Estimation of the friction coefficients
In the main channel:
Estimation of the friction coefficients
In the floodplain:
Residuals
in terms of WSE
In terms of discharge
Notes:
- High negative corelation between a0_kmin and a0_kmoy. They can be
interchangeable and the result will be the same with a weighting or
factor to compensate.
Question 1:
How to reduce the corelation between a0_kmin and a0_kmoy using only
a single event?
1st proposal: reduce the uncertainty in the observational data
Experiment: 1_WSE_floodplain_low_uncertainty
Calibration data
A sample was taken of all measurements shown previously: 
Corelation plot of MCMC cooked:
Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in m3/s, velocity in m/s kmin and kmoy in
m1/3/s.
| N |
2001.0000000 |
2001.000000 |
2.00100e+03 |
2001.000000 |
2001.000000 |
2001.000000 |
2001.000000 |
| Minimum |
107.4770000 |
24.728800 |
2.28700e-04 |
5.858510 |
5.162780 |
7.256530 |
8.535670 |
| Maximum |
128.5200000 |
47.267600 |
1.02860e-03 |
19.895200 |
19.534400 |
26.391600 |
25.783100 |
| Range |
21.0430000 |
22.538800 |
7.99900e-04 |
14.036700 |
14.371600 |
19.135100 |
17.247400 |
| Mean |
117.0700000 |
35.709300 |
4.68000e-04 |
10.422800 |
10.340100 |
15.183500 |
15.256800 |
| Median |
116.6180000 |
35.924800 |
4.40500e-04 |
10.168100 |
10.021500 |
15.076100 |
14.853100 |
| Q10% |
111.3130000 |
29.928700 |
3.08800e-04 |
7.961250 |
7.902230 |
11.555500 |
11.659700 |
| Q25% |
114.0760000 |
31.904100 |
3.64800e-04 |
9.012630 |
8.877260 |
13.179400 |
13.159800 |
| Q75% |
120.6260000 |
38.717500 |
5.48300e-04 |
11.564200 |
11.582200 |
17.017600 |
17.146600 |
| Q90% |
122.3280000 |
42.365800 |
6.64100e-04 |
13.277000 |
13.104500 |
18.888700 |
19.327900 |
| St.Dev. |
4.3978600 |
4.729290 |
1.39500e-04 |
2.099750 |
2.128930 |
2.922280 |
3.026050 |
| Variance |
19.3412000 |
22.366200 |
0.00000e+00 |
4.408930 |
4.532330 |
8.539750 |
9.156990 |
| CV |
0.0375661 |
0.132438 |
2.98147e-01 |
0.201457 |
0.205891 |
0.192464 |
0.198341 |
| Skewness |
0.1696110 |
0.105879 |
8.07301e-01 |
0.714238 |
0.737369 |
0.450935 |
0.561829 |
| Kurtosis |
-0.6100620 |
-0.633168 |
4.67690e-01 |
0.821512 |
1.008740 |
0.474089 |
0.139611 |
| MaxPost |
118.9850000 |
33.238100 |
3.34500e-04 |
9.791470 |
9.998730 |
14.983100 |
14.560200 |
| St.Dev. |
4.39786 |
4.72929 |
0.139538 |
2.09975 |
2.12893 |
2.92228 |
3.02605 |
| MaxPost |
118.98500 |
33.23810 |
0.334454 |
9.79147 |
9.99873 |
14.98310 |
14.56020 |
Estimation of the friction coefficients
In the main channel:
Estimation of the friction coefficients
In the floodplain:
Residuals
in terms of WSE
In terms of discharge
Notes:
- High negative corelation between a0_kmin and a0_kmoy. They can be
interchangeable and the result will be the same with a weighting or
factor to compensate.
Bibliography:
PROUST, SEBASTIEN, and VLADIMIR I. NIKORA. 2025.
“Dataset of a
Laboratory Study on Flows in a Compound Open Channel with Transverse
Currents.” Recherche Data Gouv.
https://doi.org/10.57745/HJKRYH.
Proust, Sébastien, and Vladimir I. Nikora. 2020.
“Compound
Open-Channel Flows: Effects of Transverse Currents on the Flow
Structure.” Journal of Fluid Mechanics 885 (February):
A24.
https://doi.org/10.1017/jfm.2019.973.
